Hello Rick,
It is not possible to add an additional field dropdown for the grid filter. However, you have 2 alternatives available to you.
The 1st option is to enable editing within the grid. Provided the field is a dropdown, the users can click on the down arrow next to the field and see the dropdown list. Keep in mind, by making the grid editable users can then go in and change values for the records. So if you don't want this happening then option 2 might be better.
The 2nd option, is to put the dropdown fields outside of the grid. This way users can see all the values in the list. You can also add actions to filter the grid based on the dropdown value selected. The down side of this, is that your screen might have a few dropdowns that make the screen look a bit untidy.